Errr, no - while that's what you see in the directory tree, that's not how it's done internally. SVN has a data model where multiple paths in the repo tree can point to the same underlying file object, so a branch requires no file copies, just updating what the directory tree looks like. Even that is done in a very efficient way. It might not quite be 40 bytes, but it is negligibly small.

This technique is in fact extremely similar to how Git works.